My client is 80% grey. She has dyed her hair a level 5 natural brown , but would like to now be a level 6. what is the best way to achieve this without having lighter roots?

You will probably have to use color remover. Otherwise, her ends will stay dark. The ends will take color faster than the roots, but the roots will lighten faster than the ends. Therefore, you *probably* should put the new color on both the roots and the ends at the same time.